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41st Aerospace Sciences Meeting and Exhibit 
6-9 January 2003, Reno, Nevada 



AIAA 2003-47 



WIND TUNNEL MEASUREMENTS AND CALCULATIONS OF 
AERODYNAMIC INTERACTIONS BETWEEN TILTROTOR AIRCRAFT 



Wayne Johnson 
Gloria K. Yamauchi 

Army /NASA Rotorcraft Division 
Moffett Field, California 



Michael R. Derby 
Alan J. Wadcock 

Aerospace Computing, Inc. 
Moffett Field, California 



Wind tunnel measurements and calculations of the aerodynamic interactions between two 
tiltrotor aircraft in helicopter mode are presented. The measured results include the roll 
moment and thrust change on the downwind aircraft, as a function of the upwind aircraft 
position (longitudinal, lateral, and vertical). Magnitudes and locations of the largest 
interactions are identified. The calculated interactions generally match the measurements, with 
discrepancies attributed to the unsteadiness of the wake and aerodynamic forces on the airframe. 
To interpret the interactions in terms of control and power changes on the aircraft, additional 
calculations are presented for trimmed aircraft with gimballed rotors. 



T aircraft thrust 

V wind tunnel speed 

X longitudinal distance between aircraft 

y lateral distance between aircraft 

z vertical distance between aircraft 

fi advance ratio, V/QR 

p air density 

o rotor solidity, Ncj-ef/^R 

Q rotor rotational speed 

Introduction 

The tiltrotor aircraft configuration has the potential 
to revolutionize air transportation by providing an 
economical combination of vertical take-off and landing 
capability with efficient, high-speed cruise flight. In 
order to achieve the goal of a major impact on 
transportation systems, it will be necessary to 
understand, and to be able to predict, the aerodynamic 
interactions involving tiltrotors. NASA Ames Research 
Center is conducting a series of wind tunnel tests 
investigating the aerodynamic interactions of tiltrotors, 
including interactions between multiple aircraft, the 
ground, and structures. This paper presents wind tunnel 
measurements and calculations of the aerodynamic 
interactions between two tiltrotor aircraft operating in 
helicopter mode. 





Notation- 


A 


rotor disk area, jtR^ 


Cref 


blade reference chord 


Cmx 


aircraft roll moment coefficient, 




Mx / pA(QR)2R 


Cp 


aircraft power coefficient, P / p(QR)^A 


Ct 


aircraft thrust coefficient, T / 2p(QR)2A 


D 


rotor diameter, 2R 


Mx 


aircraft roll moment 


N 


number of blades 


P 


aircraft power 


r 


blade radial station (0 to R) 


fc 


vortex core radius 


R 


blade radius 


s 


wing semispan 



•Presented at the 41st Aerospace Sciences Meeting and 
Exhibit, Reno, Nevada, January 6-9, 2003. Copyright © 
2003 by the American Institute of Aeronautics and 
Astronautics, Inc. No copyright is asserted in the United 
States under Title 17, U.S. Code. The U.S. Government has 
a royalty-free license to exercise all rights under the 
copyright claimed herein for Governmental purposes. All 
other rights are reserved by the copyright owner. 



1 
American Institute of Aeronautics and Astronautics 



Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 1 7, U.S. Code. 
The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. 
All other rights are reserved by the copyright owner. 



A series of aerodynamic interaction tests are being 
conducted using model tiltrotors in the Army 7- by 10- 
Foot Wind Tunnel at NASA Ames Research Center. 
Tests completed to date include: 

a) Terminal area operations: aerodynamic interactions 
between two tiltrotor aircraft, primarily at 47 knots. 

b) Terminal area operations: two aircraft, with low 
thrust on the downwind aircraft; with and without 
ground plane; flow visualization includes oil flow and 
tufts on ground plane. 

c) Hover and low speed: one aircraft, in and out of 
ground effect; including measurements of the outflow 
velocity. 

d) Single rotor (a helicopter rotor or one tiltrotor) 
upstream of a tiltrotor aircraft that is at low thrust; at 
10 knots, with and without ground plane. 

e) City operations: one aircraft in vicinity of a 
building; at 20 knots, including smoke flow 
visualization. 

f) Baseline aerodynamics: one aircraft; constant 
thrust velocity sweeps up to 70 knots, and hover 
collective sweeps; PIV measurements of wake flow 
field. 

g) Large yaw angles: in preparation for future test of 
airframe/rotor interference using a 0.25-scale model, 
assessment of mounting strut interference effects. 

For the above tests the tiltrotor model was in helicopter 
configuration, and aircraft forces and moments were 
measured in all cases. The speeds quoted above are 
equivalent full scale values. This paper presents results 
from just the first of the above subjects: the 
aerodynamic interactions between two tiltrotor aircraft. 
Such interaction may be expected to be an important 
factor in effective terminal area operations of tiltrotors. 

Calculations of the aerodynamic interactions were 
performed using CAMRAD II, which is a modem 
rotorcraft comprehensive analysis that has advanced 
models intended for application to tiltrotor aircraft as 
well as helicopters. The objectives of the calculations 
were to first establish how well the wind tunnel 
measurements can be predicted using current wake 
models; and then to interpret the interactions in terms of 
control and power changes on the aircraft. 

Test and Model Description 

Two tiltrotor models were installed in the Army 7- 
by 10-Foot Wind Tunnel at NASA Ames Research 
Center, as shown in figure 1. The key geometric 
parameters were chosen to be representative of tiltrotor 
designs: rotor planform and twist, the rotor/rotor 



separation, and the rotor/wing separation. The diameter 
of the rotors was 0.7812 ft, and the wing span was 
0.9706 ft. This corresponds to a scale of about 1/32 for 
theXV-15 orBA609; 1/49 for the V-22; and 1/110 for 
a 100-passenger tiltrotor design. 

The three-bladed rotors had counter-clockwise 
rotation on the right rotor, clockwise rotation on the 
left rotor. The tapered blades had a thrust-weighted 
solidity of a = 0.102 (with 25.5% root cutout); a total 
twist of -47.5 deg (-8 deg from 75% radius to the tip); 
and airfoil thickness ratios of 28, 18, 12, and 9% at r/R 
= 0.25, 0.50, 0.75, and 1.00 respectively. The wing 
was machined aluminum, with zero flap deflection. The 
wing semispan was 0.4853 ft. The hub and control 
system were commercially available radio-control model 
helicopter tail rotor assemblies. The rotors had 
collective pitch control, allowing trim of aircraft thrust 
and roll moment. The rotors did not have flap or lag 
hinges, or a gimbal, and did not have cyclic pitch 
control. Hence the rotors operated with some hub 
moment in edgewise flight (helicopter mode forward 
flight). The blade weight gives a Lock number of about 
7.6. Figure 2 is a drawing of the tiltrotor model. A 
fuselage (including tail) was available, but not used for 
the investigation reported here. Each aircraft had a 6- 
component balance to measure total aircraft forces and 
moments. The sting mount attached to a taper socket 
(shown aft of the wing in figure 2), which was attached 
to the balance. The electric motor (shown forward of the 
wing in figure 2) was on the metric side of the balance. 
The design rotational speed of the rotors was 6355 rpm, 
corresponding to a tip speed of 263 ft/sec. The Reynolds 
number based on the blade tip chord and speed was 
about 63000. 

The tiltrotor aerodynamic interaction investigation 
was conducted with two tiltrotor models, the downwind 
aircraft operating in the wake of the upwind aircraft. The 
aircraft were in helicopter configuration (nacelle angle 
90 deg), with the rotor shafts vertical and the wing at 
zero angle of attack and yaw. The downwind aircraft was 
mounted on a fixed sting. The upwind aircraft was 
mounted on a traverse mechanism (figure 1), allowing 
variation of its position in all three directions: 
longitudinal, lateral, and vertical (x,y,z) relative to the 
downwind aircraft. With the upwind aircraft in the 
extreme top/port position and its rotors not turning, the 
downwind aircraft was trimmed to a specified thrust and 
to approximately zero roll moment (for each 
longitudinal position tested). The collective pitch angles 
of the rotors on the downwind aircraft were then kept 
fixed as the position of the upwind aircraft was varied in 
the lateral-vertical direction. The control of the upwind 
aircraft was always adjusted as required to maintain a 



American Institute of Aeronautics and Astronautics 



specified thrust and zero roll moment. Thus the roll 
moment and thrust of the downwind aircraft are the 
primary measures of the interaction. 

The upwind aircraft position (x,y,z) was measured 
relative to the center of the downwind aircraft. The 
longitudinal separation x is specified in terms of the 
rotor diameter D, measured between corresponding 
points on each aircraft. The y and z positions are 
specified in terms of the aircraft semispan s. The lateral 
position y is positive with the upwind aircraft to 
starboard, and the vertical position is positive with the 
upwind aircraft above the downwind aircraft. The 
coefficients used are defined as follows: 

Ct/ct = T / 2pA(QR)^a 

Cux/cr = Mx / pA(QR)2Ra 

where T and Mx are the total aircraft thrust and 
moment. Note that the thrust coefficient is based on the 
area of both rotors, 2A. The roll moment is positive for 
roll right. The balance measured the load on the entire 
aircraft, including the wing. The wing download for the 
operating conditions considered is estimated to be less 
than 10% of the rotor thrust. 

Wind Tunnel Test Results 

The test results reported here consist of four runs 
(described in table 1), at nominal longitudinal separation 
distances of x/D = 2.5, 5.0, and 10.0 (two runs at x/D = 
2.5). The wind tunnel speed gave an advance ratio of 
/i= 0.10, corresponding to about 47 knots full scale. 
The rotor thrust was about Cj/a = 0.12, which was 
below stall for these small rotors (based on power 
characteristics). 

Table 1. Test conditions. 



run number 


118 


122 


123 


126 


points 


77 


87 


87 


87 


nominal x/D 


2.5 


2.5 


5.0 


10.0 


actual x/D 


2.54 


2.54 


5.08 


10.16 


/i 


0.100 


0.100 


0.100 


0.100 


downwind aircraft 








rpm 


6356 


6367 


6258 


6365 


reference condition 








Cj/o 


0.121 


0.122 


0.120 


0.122 


Cmx/ct 


0.0085 


-0.0043 


-0.0043 


-0.0056 


upwind aircraft 








rpm 


6319 


6353 


6337 


6349 


trim condition 










Cj/a 


0.121 


0.121 


0.121 


0.121 



Three data points were taken with the upwind aircraft 
at the reference position (extreme top/port, its rotors not 
turning). Then 87 points (except for run 118) were 
taken with the upwind aircraft traversing the grid shown 
in figure 3. The grid was scaled with the wing semispan 
s. The lateral position extended from y/s = -7 (forward 
aircraft to port) to y/s = +3, the vertical position from 
z/s = -1 (forward aircraft below) to z/s = +4. The 
resolution was 1 semispan, except additional points 
giving a vertical resolution of 1/2 semispan for y/s = 
±2. During the traverse over this grid, the mean 
operating condition values (rotor speed, advance ratio, 
and upwind aircraft thrust) exhibited an rms variation of 
about 1%. Note in table 1 that the downwind aircraft in 
the reference condition does not quite have zero roll 
moment. Hence the roll moment data presented are 
relative to the roll moment at this reference condition. 
Figure 4 illustrates the relative location of the two 
aircraft for lateral positions of y/s = 0, -2, and -4. 

Figure 5 shows the measured roll moment on the 
downwind aircraft, for x/D =2.5, 5.0, and 10.0. The 
largest interaction occured for lateral separation of y/s = 
±2, and z/s about 1 (upwind aircraft above downwind 
aircraft). For y/s = -2, the left rotor of the downwind 
aircraft was aligned with the right rotor of the upwind 
aircraft (figure 4b). Hence the downwind left rotor was 
in the downwash of the upwind aircraft, which produced 
a reduction in thrust on the left rotor, hence a roll 
moment to the left (negative). There was also a local 
maximum of the interaction at y/s = -4.5. At y/s = 
-4.5, the left rotor of the downwind aircraft was 
outboard of the upwind aircraft, so the downwind left 
rotor was in an upwash, producing a thrust increase and 
a roll moment to the right (positive). 

Figure 6 shows the measured change of the thrust on 
the downwind aircraft, for x/D = 2.5, 5.0, and 10.0. The 
largest interaction occured for y/s = 0, when the 
downwind aircraft was directly behind the upwind 
aircraft. The average roll moment in this condition was 
zero, but there was a significant thrust reduction, 
because the downwind aircraft was operating in the 
downwash field of the upwind aircraft. At y/s = -4.5 
there was a thrust increase, because of the upwash from 
the upwind aircraft. Note that the trim thrust value was 
Cj/a = 0.12, so the variations shown in figure 6 are 
significant. 

Figures 5 and 6 both show a generally symmetric 
variation with lateral separation y. Such symmetry is 
expected, so it serves to confirm the quality of the data. 
As the longitudinal separation increased, the interaction 
became weaker, but was still relatively strong at x/D = 
10.0. The interaction moved to slightly larger y/s, 
indicating a lateral spreading of the wake; and to larger 



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z/s, indicating downward convection of the wake (so the 
upwind aircraft was higher at the maximum interaction). 
Similar wake behavior was observed in hdar (light 
detecting and ranging) wake measurements of the XV- 15 
(reference 1). In helicopter mode at 60 and 90 knots, the 
wake was found to consist of a pair of vortices separated 
by the distance between the advancing blade tips. For 
these speeds, the decay and separation seemed to depend 
on time not distance. At 90 knots the wake maintained 
strength to x/D = 40 or so, with little spreading. At 60 
knots and x/D = 10, the lateral separation was roughly 
1.25 span, and the wake was just starting to decay. 

Rotorcraft Analysis 

The aerodynamic interaction was calculated using the 
rotorcraft comprehensive analysis CAMRAD II, which 
is an aeromechanical analysis of helicopters and 
rotorcraft that incorporates a combination of advanced 
technologies, including multibody dynamics, nonlinear 
finite elements, and rotorcraft aerodynamics. CAMRAD 
II is described in references 2-4. The wake model for 
tiltrotor performance and airloads calculations has been 
the subject of recent correlation work, summarized in 
reference 5. 

For the present investigation, four rotors were 
modelled, with fully interacting wakes. The blades were 
assumed to be rigid (no gimbal and no elastic 
deflection), with no cyclic pitch and zero shaft angle. 
The aerodynamic model used lifting-line theory with a 
vortex wake calculation of the induced velocity. The 
blade aerodynamic surfaces were represented by 10 
panels, from the root cutout of r/R =0.255 to the tip, 
with panel widths varying from O.IOIR inboard to 
0.040R at the tip. The drag coefficients in the airfoil 
tables were corrected to the lower Reynolds number of 
the model, using a factor equal to the Reynolds number 
ratio to the 1/5 -power. Inboard stall delay was accounted 
for, as described in reference 5. A full free-wake analysis 
was performed, calculating the distorted geometry of tip 
vortices from each of the three blades on all four rotors. 
Calculations are only presented for x/D = 2.5, with 16 
revolutions of wake retained behind each rotor. 

The wake model used was developed for the 
prediction of helicopter and tiltrotor performance, 
airloads, and structural loads. For such tasks many 
details of the wake model can have a significant 
influence on the calculated results. In contrast, because 
the aerodynamic phenomenon of interest here is the 
influence of a chaotic wake well downstream of the 
rotors generating the wake, most wake parameters had 
little effect on the downstream aircraft loads. A 
parameter that was found to have an influence was the 
rate of growth of the tip vortex viscous core. The 



calculations assumed a linear growth of core radius r^ 
with wake age : 

rc/c = rcO/c + (0/0l) 

where c is the blade chord, and 0i is the wake age where 
the core increment equaled the chord. An initial value of 
r^^Q/c = 1.0 was used, with a maximum core radius of 
VqIc = 10. The baseline calculations used (^i = 1.5 
revolutions. 

The calculations were performed in the same manner 
as the test procedures. The collective pitch of the 
downwind rotors was fixed at a value that gave the 
measured reference thrust and zero roll moment without 
the interaction of the upwind rotors. During the 
traverse, the upwind rotors were trimmed to the 
measured thrust (Cj/a= 0.118) and zero roll moment. 
The calculations were performed for a lateral and vertical 
resolution of 1/2 semispan. The calculated thrust 
presented is the sum of the thrust of the two downwind 
rotors. The calculated roll moment presented is that 
produced by the thrust of the two downwind rotors, plus 
the roll moments at the hubs of these two rotors. The 
analysis did not include a wing or fuselage. 

Correlation Results 

Figure 7 compares the measured and calculated roll 
moment on the downwind aircraft, for x/D =2.5 and 
/i = 0.1. The measured results are the average of the data 
for positive and negative y (with appropriate sign 
changes), from run 122. The calculations exhibit the 
maxima at about y/s = 2 and 4.5, as observed in the 
test. The magnitude of the peak moment at y/s = 2 
matches well, although the calculated shape of the 
interaction region is different. The magnitude of the 
peak moment at y/s = 4.5 is underpredicted. The 
calculations also show a local maximum at y/s = 1 and 
z/s = 2.5, which is not found in the measurements. It is 
believed that this discrepancy is associated with the 
unsteadiness of the flow field. The calculations were 
performed assuming that the wake geometry and 
resulting loading were perfectly periodic, but for the 
downwind aircraft directly behind the upwind aircraft (y 
near zero) a converged periodic solution became 
increasingly difficult to obtain. 

Figure 8 compares the measured and calculated thrust 
change on the downwind aircraft, for x/D = 2.5 and /i = 
0.1. The measured and calculated results show similar 
patterns, but the magnitude of the calculated thrust 
change is about one-half that measured. This difference 
perhaps reflects the influence of the wake on the wing 
and body of the aircraft, which were not included in the 
analysis. 



American Institute of Aeronautics and Astronautics 



Figure 9 shows top and side views of the calculated 
wake geometry, for y/s = 2 and z/s = 1. For clarity, 
only one of the three tip vortices from each rotor is 
plotted. Note that the outer two rotors show relatively 
little downward convection of the wake. The wake from 
the port upwind rotor is ingested into the starboard 
downwind rotor, and the wakes from both rotors are 
convected downward faster. Preliminary examination of 
PIV measurements of the wake formation at 2.5D 
downstream of a single tiltrotor model (without the 
downwind aircraft) showed two super- vortices, with a 
lateral separation of about 1.20 times the aircraft span 
(between rotor edges). The calculated wake geometry 
showed a similar magnitude of lateral spreading of the 
wake. 

Figure 10 examines the influence of the tip vortex 
core growth rate on the calculated roll moment, for y/s 
= ±2. The baseline calculations used 0i =1.5 revs; the 
faster and slower growth cases were for 0i = 1.0 and 2.0 
respectively. Faster rate of core growth had little 
influence. With a slower rate of core growth, hence 
stronger interactions of the tip vortices in the wake, the 
calculated results are more erratic, reflecting a more 
chaotic wake geometry. The trend and magnitude of the 
calculated roll moment was about the same even with 
the slower core growth, but the sensitivity suggests that 
the unsteadiness of the interaction be further 
investigated. 

Figure 11 shows the influence of the rotor hub 
moment on the aircraft roll moment, for y/s = ±2. The 
baseline results are for the rigid rotor, hence include the 
hub moments. The roll moment obtained considering 
just the rotor thrust changes is also shown, and 
indicates that the hub moment contribution to the total 
is small. Figure 1 1 also shows the aircraft roll moment 
calculated with a gimballed rotor, for which the hub 
moment is zero. The introduction of a gimbal has some 
influence, because the flapping of the rotor relative to 
the shaft is not zero (cyclic pitch was still not used). 
The influence of the Reynolds number correction was 
also examined, and was found to be small, since these 
interactions involve principally lift changes on rotors 
operating below stall. 

In order to interpret the magnitude of the interactions 
observed, calculations were performed of the control 
required to maintain trim of the downwind aircraft. For 
these calculations a gimballed rotor was used, and the 
Reynolds number correction omitted. The geometry of 
the rotor and aircraft were not changed. Both aircraft 
were trimmed to Cjlo = 0.120 and zero roll moment. 
Figures 12a and 12b show the calculated lateral control 
(differential collective) and collective control changes on 
the downwind aircraft, for ^ = 0.1 and x/D =2.5, when 



the downwind aircraft is trimmed to constant thrust and 
zero roll moment. The lateral control (differential 
collective) change reflects the roll moment of the 
untrimmed aircraft, and ranges from -1.9 to 0.35 deg. 
The collective change reflects the aircraft thrust, and 
ranges from -0.8 to 2.9 deg. These control increments 
produced by the interaction are significant, but within 
the control authority of typical tiltrotor designs. Figure 
12c shows the influence of the interaction on 
performance. The calculated change of the power 
coefficient ranges from ACp/a = -0.0020 to 0.0065, 
relative to a baseline Cp/a = 0.0180. (For a 40000 lb 
tiltrotor, the aircraft power change is -600 to 1800 hp.) 
The power change is also a reflection of the thrust 
change of the untrimmed aircraft. Such performance 
changes are interesting, but probably of limited practical 
utility. 

Concluding Remarks 

Wind tunnel measurements and calculations of the 
aerodynamic interactions between two tiltrotor aircraft 
in helicopter mode have been presented. The measured 
roll moment on the downwind aircraft was largest when 
the left rotor of the downwind aircraft was operating in 
the down wash from the right rotor of the upwind aircraft 
(or the downwind right rotor operating in the downwash 
from the upwind left rotor). The measured thrust 
decrease was largest when the downwind aircraft was 
directly behind the upwind aircraft. There was also a 
local maximum in the roll moment, and a thrust 
increase, when the downwind aircraft was outboard of 
the upwind aircraft. 

The calculated roll moment on the downwind aircraft 
matched the magnitude and location of the measured 
peak. The calculations also showed a local maximum in 
roll moment, not observed in the test, when the 
downwind aircraft was nearly aligned with the upwind 
aircraft. This discrepancy may be associated with the 
unsteady nature of the wake. The calculated thrust 
change on the downwind aircraft matched the pattern of 
the measurements, but the magnitude was smaller than 
measured, perhaps because the forces on the wing and 
body of the aircraft were not included in the analysis. 

Calculations were performed of the control required 
to maintain trim of the downwind aircraft, including 
gimballed rotors. The lateral control (differential 
collective) reflected the roll moment on the untrimmed 
aircraft, and the collective control and power changes 
reflected the thrust change on the untrimmed aircraft. 
The control increments produced by the interaction were 
significant, but within the control authority of typical 
tiltrotor designs. 



American Institute of Aeronautics and Astronautics 



References 

1) Schillings, JJ.; Ferguson, S.W.; Brand, A.G.; 
Mullins, B.R.; Libby, J.; "Wake Vortex Measurements 
of the XV- 15 Tiltrotor Using a Mobile Ground-Based 
Lidar System." AHS International 57th Annual Forum 
Proceedings, Washington, D.C., May 2001. 

2) Johnson, W. "Technology Drivers in the 
Development of CAMRAD II." American Helicopter 
Society Aeromechanics Specialists Conference, San 
Francisco, California, January 1994. 

3) Johnson, W. "A General Free Wake Geometry 
Calculation for Wings and Rotors." American 
Helicopter Society 51st Annual Forum Proceedings, 
Fort Worth, Texas, May 1995. 

4) Johnson, W. "Rotorcraft Aerodynamics Models for a 
Comprehensive Analysis." AHS International 54th 
Annual Forum Proceedings, Washington, D.C., May 
1998. 

5) Johnson, W. "Influence of Wake Models on 
Calculated Tiltrotor Aerodynamics." American 
Helicopter Society Aerodynamics, Acoustics, and Test 
and Evaluation Technical Specialists Meeting, San 
Francisco, CA, January 2002. 




Figure 1. Tiltrotor models in the Army 7- by 10-Foot 
Wind Tunnel at NASA Ames Research Center. 




Figure 2. Drawing of tiltrotor model (wind tunnel flow 
from left to right). 



4. 

^ 2 
0. 

-2. 









X 


reference point 












o 


data points 








-X 


o 


o 


o 


o o o o 
o 


o 


o 
o 


o 


o 


o 


o 


o 


o o o o 
o 


o 


o 
o 


o 


— o 


o 


o 


o 


o o o o 
o 


o 


o 
o 


o 


o 


o 


o 


o 


o o o o 
o 


o 


o 
o 


o 


— o 


o 


o 


o 


o o o o 
o 


o 


o 
o 


o 


o 


o 

1 


o 


o 

1 


o o o o 

1 1 


o 


o 

1 


o 

1 



-6. 



-2. 
y/s 



Figure 3. Grid of measurement locations (position of 
upwind aircraft relative to downwind aircraft). 



American Institute of Aeronautics and Astronautics 




(a) y/s = 




(b) y/s = -2 





-0.04 -0.02 0.00 0.02 0.04 



(a) x/D = 10.0 




-0.04 -0.02 0.00 0.02 0.04 



(b) x/D = 5.0 




-0.04 -0.02 0.00 0.02 0.04 

(c) x/D = 2.5 

Figure 5. Measured roll moment coefficient Cyi^/o of 
downwind aircraft, at ^ = 0.1, as function of upwind 



(c) y/s = -4 

Figure 4. Illustrations of the relative positions of the aircraft position (contour increment = 0.01, dashed line 



two aircraft. 



for negative). 



American Institute of Aeronautics and Astronautics 





-0.03 -0.02 -0.01 0.00 0.01 



(a) x/D = 10.0 



-0.02 0.00 0.02 0.04 



(a) measured 





-0.03 -0.02 -0.01 0.00 0.01 



(b) x/D = 5.0 




-0.02 0.00 



0.02 



0.04 



(b) calculated 

Figure 7. Comparison of measured and calculated roll 
moment coefficient Cmx/<^ of down wind aircraft, at ^ = 
0.1 and x/D = 2.5 (contour increment = 0.01, dashed 
line for negative). 



-0.03 -0.02 -0.01 0.00 0.01 

(c) x/D = 2.5 

Figure 6. Measured thrust change ACj/a of downwind 
aircraft, at fi = 0.1, as function of upwind aircraft 
position (contour increment = 0.005, dashed line for 
negative). 



American Institute of Aeronautics and Astronautics 




-0.03 -0.02 -0.01 0.00 0.01 



(a) measured 




-0.03 -0.02 -0.01 0.00 



0.01 



downwind, left rotor 
downwind, right rotor 
upwind, left rotor 
upwind, right right 




a) top view 




(b) calculated 

Figure 8. Comparison of measured and calculated thrust 
change ACx/cr of downwind aircraft, at ^ = 0.1 and x/D 
= 2.5 (contour increment = 0.004, dashed line for 
negative). 



b) view from starboard 

Figure 9. Calculated wake geometry, at /i = 0.1, x/D = 

2.5, y/s =2, z/s = 1 (only one tip vortex from each 
rotor shown). 



American Institute of Aeronautics and Astronautics 



D RunllS, y/s = -2 

O Run 122, y/s = -2 

A Run 118, y/s = +2 

V Run 122, y/s = +2 

baseline calculated 

faster core growth 

slower core growth 



0.06 



S 0.04 - 

U 






O 

a 



0.02 



- 0.00 



-0.02 




0. 1. 2. 3. 

vertical position, z/s 



4. 



Figure 10. Influence of tip vortex core growth on 
calculated roll moment of downwind aircraft, at ^ = 0.1, 

x/D = 2.5, y/s = ±2. 



□ Run 118, y/s = -2 
O Run 122, y/s = -2 
A Run 118, y/s = +2 
V Run 122, y/s = +2 
baseline calculated 
without hub moment 
gimballed rotor 



X 

U 

a 

a 

o 



0.06 



0.04 



0.02 - 



- 0.00 



-0.02 




0. 1. 2. 3. 

vertical position, z/s 



4. 



Figure 11. 
moment of 

y/s = ±2. 



Influence of hub moment on calculated roll 
downwind aircraft, at jj. = 0.1, x/D = 2.5, 




-2.0 -1.0 0.0 

(a) lateral control (differential collective. 



1.0 



deg) 




-1.5 0.0 

(b) collective change (deg) 



1.5 



3.0 




-0.003 



0.000 



0.003 



0.006 



(c) power change, ACp/a 

Figure 12. Calculated control and performance changes 
of downwind aircraft, when trimmed to specified thrust 
and zero roll moment, at ^ = 0.1 and x/D = 2.5 (contour 
increment = 0.5 deg for control, 0.001 for power 
coefficient; dashed line for negative). 



10 



American Institute of Aeronautics and Astronautics